The sentence that uses correct subject-verb agreement is:
The cat carefully steps across the fence.
The other sentences contain subject-verb agreement errors. For instance, "My brother always want to cook dinner" should be "My brother always wants to cook dinner," "My teachers often gives homework on the weekend" should be "My teachers often give homework on the weekend," and "The clouds swiftly moves across the sky" should be "The clouds swiftly move across the sky."